The Ag/Si(111) 3x3 structure is known as a honeycomb-chained-triangle (HCT) structure at room temperature and an inequivalent-triangle (IET) structure at low temperature (~60K). In this work, surface phase transition of Ag/Si(111) 3x3 HCT to IET structure is studied by reflection high-energy electron diffraction (RHEED). Temperature dependence of RHEED rocking patterns were measured during cooling process of substrate, and the following results are obtained. RHEED rocking curves show continuous change during cooling process of the substrate and temperature dependence of rod intensities show discontinuity in their gradient at 150K. Streak intensities of fractional spots at low temperature increases at low temperature, which suggests smaller domain size of 3x3 structure caused by HCT to IET phase transition. It is concluded that critical temperature of structural phase transition from HCT to IET structure is 150K. In addition, atomic arrangement of HCT structure at just above the critical temperature is different from that at room temperature but similar to IET structure just below the critical temperature except for stable rotation angle of Ag/Si triangles. It is considered that order-disorder transition of IET structure occurs at lower temperature than 120K.